T. Ahsanullah, D. Gauld, J. Al-Mufarrij, F. Al-Thukair
{"title":"富格值拓扑群","authors":"T. Ahsanullah, D. Gauld, J. Al-Mufarrij, F. Al-Thukair","doi":"10.1142/S1793005714500021","DOIUrl":null,"url":null,"abstract":"In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enriched cl-premonoid and present a category SL-NTopGrp, of stratified enriched cl-premonoid-valued neighborhood topological groups. We produce some characterization theorems, and prove that every stratified L-neighborhood topological group is uniformizable. Finally, we look at the enriched lattice-valued neighborhood topological group when the underlying basis is changed under certain functorial mechanism.","PeriodicalId":44835,"journal":{"name":"New Mathematics and Natural Computation","volume":"10 1","pages":"27-53"},"PeriodicalIF":0.7000,"publicationDate":"2014-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S1793005714500021","citationCount":"6","resultStr":"{\"title\":\"ENRICHED LATTICE-VALUED TOPOLOGICAL GROUPS\",\"authors\":\"T. Ahsanullah, D. Gauld, J. Al-Mufarrij, F. Al-Thukair\",\"doi\":\"10.1142/S1793005714500021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enriched cl-premonoid and present a category SL-NTopGrp, of stratified enriched cl-premonoid-valued neighborhood topological groups. We produce some characterization theorems, and prove that every stratified L-neighborhood topological group is uniformizable. Finally, we look at the enriched lattice-valued neighborhood topological group when the underlying basis is changed under certain functorial mechanism.\",\"PeriodicalId\":44835,\"journal\":{\"name\":\"New Mathematics and Natural Computation\",\"volume\":\"10 1\",\"pages\":\"27-53\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2014-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1142/S1793005714500021\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"New Mathematics and Natural Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S1793005714500021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Mathematics and Natural Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S1793005714500021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enriched cl-premonoid and present a category SL-NTopGrp, of stratified enriched cl-premonoid-valued neighborhood topological groups. We produce some characterization theorems, and prove that every stratified L-neighborhood topological group is uniformizable. Finally, we look at the enriched lattice-valued neighborhood topological group when the underlying basis is changed under certain functorial mechanism.
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